Okazaki is a city of parks, and in most residential areas there is always a small park (koen)within a few minutes walk. These provide kids with a place to play, and when the weather is fine(and the kids in school) a nice place to lie down in the sun or read a book while listening to the birds. Or just doing nothing.
There are also several large parks. The park that tends to get the most attention is Okazaki Koen, which is where the castle is located. Obviously the focus is the castle itself, with its museum and gardens, but when the riverbanks are included, what you have is a very large tract of greenery in the heart of the city. The park has tennis courts and plenty of room for everything from riding bikes to throwing frisbees. For recreation though, some of the other parks have a lot more to offer.
A special way of relaxing that every visitor to Japan should at least experience once is going to an onsen. In the southern part of Okazaki, next to Minami Koen, there is the Wakamatsu Onsen with good access by car and public transportation and prices are reasonable as well.